بسم الله الرحمن الرحيم Advanced Control Lecture one Mohammad Ali Fanaei Dept. of Chemical Engineering Ferdowsi University of Mashhad Reference: Smith & Corripio, “Principles and practice of automatic process control, 3 rd ed., Wiley, 2006

Structures Objectives Control objectives and structures Safety Environmental protection Equipment protection Smooth plant operation and production Product quality Profit optimization Feedback Feedforward Feedback/Feedforward

Feedback control Sensor Transmitter Controller Final Control Element Process Final element SensorController Other outputsDisturbances Controlled variable Manipulated variable

Advantages and disadvantages of feedback control Advantages Very simple technique Effective for all disturbances Provides zero ss offset Works with minimum knowledge of the process Disadvantages Does not take control action until the process output has deviated from set point Affects the closed-loop stability

Feedforward control

Advantages and disadvantages of feedforward control Advantages Compensates for a disturbance before the process output is affected Does not affect the stability of the control system Disadvantages Can not eliminate steady-state offset Requires a sensor and model for each disturbance

Feedback / feedforward control

Modeling (relation between inputs and outputs of process) We can tune the controller only after the process steady-state and dynamic characteristics are known. Types of model White box (first principles) black box (empirical) Linear non-linear Static dynamic Distributed lumped Time domain frequency domain Continuous discrete For further reading refer to : R offel & Beltlem, “Process dynamics and control”, Wiley, 2006

A modeling procedure 1. Define goals Specific design decisions Numerical values Functional relationships Required accuracy 2. Prepare information Sketch process and identify system Identify variables of interest State assumptions and data 3. Formulate model Conservation balances Constitutive equations Rationalize Check degrees of freedom Dimensionless form 4. Determine Solution Analytical Numerical 5. Analyze results Check results for correctness Limiting and approximate answers Accuracy of numerical method Interpret results Plot solution Characteristic behavior Relate results to data and assumptions Evaluate sensitivity Answer “what if” questions 6. Validate model Select key values for validation Compare with experimental results Compare with results from more complex model For further reading refer to : Marlin, “Process Control”, McGraw-Hill, 2 nd Ed., 2000.

Example 1. Isothermal CSTR F CAoF CAo F VCACA Define Goals 1.Dynamic response of a CSTR to a step in the inlet concentration. 2.The reactant concentration should never go above 0.85 mole/m 3 3.When the concentration reaches 0.83 mole/m 3, would a person have enough time to respond? What would a correct response be? 1.The system is the liquid in the tank (as shown in Fig.). 2.The important variable is the reactant concentration in the reactor. Prepare Information

Example 1. Isothermal CSTR Prepare Information … 3.Assumptions Well-mixed vessel Constant density Constant flow in Constant temperature 4.Data F = m 3 /min, V = 2.1 m 3 (C Ao ) initial = mole/m 3,  C Ao = mole/m 3 The reaction rate is r A = -kC A, with k = 0.04 min -1 F CAoF CAo F VCACA

Example 1. Isothermal CSTR F CAoF CAo F VCACA Formulate Model 1.Material balance: 2.Rationalize : 3.Degrees-of-freedom: One equation, one variable(C A ), two external variables (F and C Ao ) and two parameters (V and k). Since the DOF are zero, and the model is exactly specified.

Example 1. Isothermal CSTR F CAoF CAo F VCACA Analytical Solution Numerical Solution

Example 1. Isothermal CSTR